$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 3$ and $ JT = 2x + 25$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 3} = {2x + 25}$ Solve for $x$ $ 4x = 28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({7}) - 3$ $ JT = 2({7}) + 25$ $ CJ = 42 - 3$ $ JT = 14 + 25$ $ CJ = 39$ $ JT = 39$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {39} + {39}$ $ CT = 78$